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feat(CategoryTheory/Adhesive): coslices of adhesive categories are adhesive #42973

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feat(CategoryTheory/Adhesive): coslices of adhesive categories are adhesive #42973

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10 changes: 6 additions & 4 deletions Mathlib/CategoryTheory/Adhesive/Over.lean
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Expand Up @@ -11,10 +11,7 @@ public import Mathlib.CategoryTheory.Limits.Constructions.Over.Connected
/-! # Adhesive structure on slice categories

The slice category `Over B` inherits the property of being adhesive from the
base category.

## TODO
- The dual result for `Under B`.
base category, and dually so does the coslice category `Under B`.
-/

public section
Expand All @@ -30,4 +27,9 @@ instance adhesive_over [Adhesive C] [HasPullbacks C] [HasPushouts C] (B : C) :
Adhesive (Over B) :=
adhesive_of_preserves_and_reflects_isomorphism (Over.forget B)

/-- Coslices of adhesive categories are adhesive. See [adhesive2004], Proposition 8 (ii). -/
instance adhesive_under [Adhesive C] [HasPullbacks C] [HasPushouts C] (B : C) :
Adhesive (Under B) :=
adhesive_of_preserves_and_reflects_isomorphism (Under.forget B)

end CategoryTheory
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